Hi, my problem is the next differential equation:

In maple. I used this code to solved it, but throws this error:

dsolve({diff(y(x), x, x) = -P*x/(I*E), eval(y(x), x = L) = 0, eval((D(y))(x), x = L) = 0});
Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: {y(L), y(x)}

What is the problem with my code? How can solve my ODE with tis boundary conditions? 

How to write down the differential equation for this practical question? 

I can use dsolve to solve the system equation. 

Thank you! 

EDIT TIME: 14:30 CET

where P(1) and P(2) are NxN matrix functions.

My trial code for STEP 0

 alpha times integral w.r.t. x

 Int_x__alpha:=proc(term,alpha): 
 return
select(has,term,x).P(alpha)^T.remove(has,term,x)
end proc: 

 alpha times integral w.r.t. t

Int_t__alpha:=proc(term,alpha):   #alpha times integral w.r.t. t
 return
remove(has,term,t).P(alpha).select(has,term,t)
end proc:

when I run the last procedure for the testing

 Int_t__alpha(Psi(x)^T.C. Psi(t),2);

I get

But it must be 

Because the multiplication is not commutative in Matrices. So, the last procedure must be corrected. 

DETAILS for the procedures:

-------------------------------------------------------------------------------------------------------------------------------------

MAIN QUESTION:

Suppose that we have a PDE as follows 

                                             ...(3)

subject to appropriate Initial and Boundary conditions.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 1

• Find the highest derivative w.r.t. x and w.r.t. t. Then, Let the trial function be the summation derivative of these highest derivatives. I mean

Trial Function:                                           ...(4)

where Psi(x), Psi(t) are Nx1 vectors and C is a NxN matrix.

I can't write a maple code for selecting the trial function.  May be you can.

trial_function:=diff(u(x,t),x,t)=Psi(x)^T.C. Psi(t); 

# I deliberately used ^T instead of ^+ for Transpose.
# If I use ^+, the transpose sign doesn't appear in 2d output. May be you have an other idea.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 2

• Integrate the Eq.4  w.r.t. t from 0 to t, we have

STEP2:=int(  lhs(trial_function) ,t=0..t)=Int_t__alpha(rhs(trial_function),1);


The code must be improved. Firstly, substitute t=s in lhs(trial_function) and then integrate s=0..t 

-------------------------------------------------------------------------------------------------------------------------------------

STEP 3

int(lhs(STEP2),x=0..x)= Int_x__alpha(rhs(STEP2),1);

The code must be improved.

-------------------------------------------------------------------------------------------------------------------------------------
STEP 4

• Integrate Eq.4 w.r.t x

-------------------------------------------------------------------------------------------------------------------------------------
STEP 5

• Substitute Eq. (5), Eq. (6), Eq. (7) to Eq. (3),
• I mean substituting  u_x(x,t), u_t(x,t), u(x,t) to PDE.

-------------------------------------------------------------------------------------------------------------------------------------

STEP 6

DOWNLOAD ALL MAPLE CODE: all_code.mw

How can I get Maple to simplify expressions into more meaningful forms?

For example, 

xc1 := -(2*Q*R1 + sqrt(4*Q^2*R1*RL - R1^2 + 2*R1*RL - RL^2))*R1/(4*Q^2*R1 + R1 - RL)

The numerator, under the radical, is more meaningful as sqrt(4 Q^2 R1 RL-(R1-RL)^2).

Similarly, the denominator can be simplified to Rs(4 Q^2+1)-RL.  

How do I get Maple to get me there?

I am wondering if there are examples of agent-based models in economics domain that have been implemented in Maple.

Any infomration/source is more than welcome!

Thanks in advance

I actually want to numerically solve Karhunen-Loeve Decomposition, which is reduced to homogenous Fredholm integral equation second kind when the kernel is the function of correlation of variables, by using any procedures (Galerkin is better if it is availabe). FYI, with "intsolve" I just got f(x)=0. 

I am a newbie in Maple! I tried both ThermophysicalData and its CoolProp package to find saturation pressure of vapor for given air-water mixture temperature.

I want to calculate water vapor density in air or simply Absolute humidity (kg/m3)

But i can not see any meaningful function or combination of functions/properties in CoolProp to give such output.

P_w in CoolProp, HApropSI takes this as input only that is not usefule either way inpoutput

The rationale is to work from RH and then calculate P_w as output: P_w=RH x P_g where P_g is vapor saturation pressure at the given ambient condition.

From there all world is yours!

You can use ideal gas rules to do everything. But i cant use CoolProp to calculate the ABsolute humidty for given RH and ambient condition.

Note that clearly i can calculate all these from hand calculation as well as approximation formuale of Clausius-Clapeyron equation. But i wanted to do in Maple with its packages.

Any help is appreciated!?

Regards

Sina

Hi

I have the following fractional  system of differential equation. How to plot it for alpha=0.5, beta=0.5?

eq1:=diff(y1(t),t$alpha)=0.04-(0.09*y1(t)*y2(t))-(0.00250*y1(t)*y2(t))/((0.03500+y2(t)))-0.04*y1(t);                                                                                                                                                                    

eq2:=diff(y2(t),t$beta)=(0.09*y1(t)*y2(t))+(0.00250*y1(t)*y2(t))/((0.035+y2(t)))-(0.02+0.04)*y2(t);

Hi, 

Whenever I open Maple 2020 and type one single letter or number (doesn't matter) Maple 2020 will "freeze" and load forever (i have had it open for a long time, just watching that f**king blue circle spin...

I have tried reinstalling, repairing, running as admin, and changing the compatibility mode, still, nothing works:(

I run Maple 2020 as a Student with WithGym

Pc specs:

Intel i5-10300h 2.6 ghz

Geforce 1660 ti 6gb

Windows 10 x64

Is it possible in one worksheet of a workbooks to access variables or embedded components in another worksheet programmatically?

As far as I can see it is possible to save and restore variables through the variable browser, so it is also possible to get them from one worksheet to another. This is however done by the user.

Now the question is, if it is somehow possible to e.g. access the contents of a embedded component like a Combobox in a different worksheet of the workbook - without opening the worksheet first?

[[1,1,["ab","xy"]], [0,1,["xy"]]]
 

how to sort by first number , second number , and list of string ?

how to count and group by third list of strings having first two number 0,0 or 0,1 or 1,0 or 1,1 

for example 

["xy"] at most count 4  , at least count 1

would like to find which is [1,1,... ] and only count 1

Suppose we have a 200-litre tank. Suppose 10 litres per minute of salt water (brine) flows into the tank at the top, it mixes perfectly with the contents of the tank, and 10 litres per minute of the mixture flows out of the tank at the bottom. Assume for simplicity that the salt water in the tank is stirred so that its concentration is uniform in the tank. Let S(t) be the amount of salt, in grams, in the tank at t time minutes. Suppose the salt water flowing into the tank has concentration 80 grams per litre.

Find the differential equation to model the change in S(t).

Assuming that at t = 0 time the concentration of salt in the tank is 10 grams per litre, solve the differential equation using Maple.

What is S(infinite)? That is, how much salt is in the tank after a long time?

Now graph S(t) for a suitable domain so we can see the function approaching the value S(infinite)

---------------------

Have some difficulty to understand the problem. I mean, such modelling problem rather than pure math computation.

Thank you so much!

Let's say you make a tabulate of plots (using tabulate, because you don't want equal space for your plots as in array-plot etc). Then how should one save or export the final result as one eps or pdf file? When I right click and choose export, it only save one cell of the tabulate alone.

Hi!

Does it exist a command in the LieAlgebras package to find the list of normal subalgbras of a given finite dimensional Lie algebra?

Thank.

Hi!

I used the command "Decompose" for the following trivial 2 dimensional abelian Lie algebra:

This command returns an error:

Alg:=[D_x,D_y]:
Alg_L:=LieAlgebraData(Alg):
DGsetup(Alg_L):
Decompose();

Error, (in print/_DG) final value in for loop must be numeric or character

Why this issue?

Thanks